/*
    This code has been written by MinakoKojima, feel free to ask me question. Blog: http://www.shuizilong.com/house
    Template Date: 2015.10.12
    Note: ...
*/
 
#pragma comment(linker, "/STACK:36777216")
//#pragma GCC optimize ("O2")
#define LOCAL
#include <functional>
#include <algorithm>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iomanip>
#include <numeric>
#include <cstring>
#include <climits>
#include <cassert>
#include <complex>
#include <cstdio>
#include <string>
#include <vector>
#include <bitset>
#include <queue>
#include <stack>
#include <cmath>
#include <ctime>
#include <list>
#include <set>
#include <map>
 
//#include <tr1/unordered_set>
//#include <tr1/unordered_map>
//#include <array>
 
using namespace std;
 
#define REP(i, n) for (int i=0;i<n;++i)
#define FOR(i, a, b) for (int i=a;i<b;++i)
#define DWN(i, b, a) for (int i=b-1;i>=a;--i)
#define REP_1(i, n) for (int i=1;i<=n;++i)
#define FOR_1(i, a, b) for (int i=a;i<=b;++i)
#define DWN_1(i, b, a) for (int i=b;i>=a;--i)
#define REP_C(i, n) for (int n____=n,i=0;i<n____;++i)
#define FOR_C(i, a, b) for (int b____=b,i=a;i<b____;++i)
#define DWN_C(i, b, a) for (int a____=a,i=b-1;i>=a____;--i)
#define REP_N(i, n) for (i=0;i<n;++i)
#define FOR_N(i, a, b) for (i=a;i<b;++i)
#define DWN_N(i, b, a) for (i=b-1;i>=a;--i)
#define REP_1_C(i, n) for (int n____=n,i=1;i<=n____;++i)
#define FOR_1_C(i, a, b) for (int b____=b,i=a;i<=b____;++i)
#define DWN_1_C(i, b, a) for (int a____=a,i=b;i>=a____;--i)
#define REP_1_N(i, n) for (i=1;i<=n;++i)
#define FOR_1_N(i, a, b) for (i=a;i<=b;++i)
#define DWN_1_N(i, b, a) for (i=b;i>=a;--i)
#define REP_C_N(i, n) for (int n____=(i=0,n);i<n____;++i)
#define FOR_C_N(i, a, b) for (int b____=(i=0,b);i<b____;++i)
#define DWN_C_N(i, b, a) for (int a____=(i=b-1,a);i>=a____;--i)
#define REP_1_C_N(i, n) for (int n____=(i=1,n);i<=n____;++i)
#define FOR_1_C_N(i, a, b) for (int b____=(i=a,b);i<=b____;++i)
#define DWN_1_C_N(i, b, a) for (int a____=(i=b,a);i>=a____;--i)
 
#define ECH(it, A) for (__typeof((A).begin()) it=(A).begin(); it != (A).end(); ++it)
#define rECH(it, A) for (__typeof((A).rbegin()) it=(A).rbegin(); it != (A).rend(); ++it)
#define REP_S(i, str) for (char*i=str;*i;++i)
#define REP_L(i, hd, suc) for (int i=hd;i;i=suc[i])
#define REP_G(i, u) REP_L(i,hd[u],suc)
#define REP_SS(x, s) for (int x=s;x;x=(x-1)&s)
#define DO(n) for ( int ____n = n; ____n-->0; )
#define REP_2(i, j, n, m) REP(i, n) REP(j, m)
#define REP_2_1(i, j, n, m) REP_1(i, n) REP_1(j, m)
#define REP_3(i, j, k, n, m, l) REP(i, n) REP(j, m) REP(k, l)
#define REP_3_1(i, j, k, n, m, l) REP_1(i, n) REP_1(j, m) REP_1(k, l)
#define REP_4(i, j, k, ii, n, m, l, nn) REP(i, n) REP(j, m) REP(k, l) REP(ii, nn)
#define REP_4_1(i, j, k, ii, n, m, l, nn) REP_1(i, n) REP_1(j, m) REP_1(k, l) REP_1(ii, nn)
 
#define ALL(A) A.begin(), A.end()
#define LLA(A) A.rbegin(), A.rend()
#define CPY(A, B) memcpy(A, B, sizeof(A))
#define INS(A, P, B) A.insert(A.begin() + P, B)
#define ERS(A, P) A.erase(A.begin() + P)
#define LBD(A, x) (lower_bound(ALL(A), x) - A.begin())
#define UBD(A, x) (upper_bound(ALL(A), x) - A.begin())
#define CTN(T, x) (T.find(x) != T.end())
#define SZ(A) int((A).size())
#define PB push_back
#define MP(A, B) make_pair(A, B)
#define PTT pair<T, T>
#define Ts *this
#define rTs return Ts
#define fi first
#define se second
#define re real()
#define im imag()
 
#define Rush for(int ____T=RD(); ____T--;)
#define Display(A, n, m) {                      \
  REP(i, n){                                    \
        REP(j, m-1) cout << A[i][j] << " ";     \
        cout << A[i][m-1] << endl;                \
    }                                            \
}
#define Display_1(A, n, m) {                    \
    REP_1(i, n){                                \
        REP_1(j, m-1) cout << A[i][j] << " ";   \
        cout << A[i][m] << endl;                \
    }                                            \
}
 
typedef long long LL;
//typedef long double DB;
typedef double DB;
typedef unsigned uint;
typedef unsigned long long uLL;
 
typedef vector<int> VI;
typedef vector<char> VC;
typedef vector<string> VS;
typedef vector<LL> VL;
typedef vector<DB> VF;
typedef set<int> SI;
typedef set<string> SS;
typedef map<int, int> MII;
typedef map<string, int> MSI;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<PII> VII;
typedef vector<VI> VVI;
typedef vector<VII> VVII;
 
template<class T> inline T& RD(T &);
template<class T> inline void OT(const T &);
//inline int RD(){int x; return RD(x);}
inline LL RD(){LL x; return RD(x);}
inline DB& RF(DB &);
inline DB RF(){DB x; return RF(x);}
inline char* RS(char *s);
inline char& RC(char &c);
inline char RC();
inline char& RC(char &c){scanf(" %c", &c); return c;}
inline char RC(){char c; return RC(c);}
//inline char& RC(char &c){c = getchar(); return c;}
//inline char RC(){return getchar();}
 
template<class T> inline T& RDD(T &);
inline LL RDD(){LL x; return RDD(x);}
 
template<class T0, class T1> inline T0& RD(T0 &x0, T1 &x1){RD(x0), RD(x1); return x0;}
template<class T0, class T1, class T2> inline T0& RD(T0 &x0, T1 &x1, T2 &x2){RD(x0), RD(x1), RD(x2); return x0;}
template<class T0, class T1, class T2, class T3> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3){RD(x0), RD(x1), RD(x2), RD(x3); return x0;}
template<class T0, class T1, class T2, class T3, class T4> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5); return x0;}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline T0& RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6){RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6); return x0;}
template<class T0, class T1> inline void OT(const T0 &x0, const T1 &x1){OT(x0), OT(x1);}
template<class T0, class T1, class T2> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2){OT(x0), OT(x1), OT(x2);}
template<class T0, class T1, class T2, class T3> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3){OT(x0), OT(x1), OT(x2), OT(x3);}
template<class T0, class T1, class T2, class T3, class T4> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3, const T4 &x4, const T5 &x5, const T6 &x6){OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);}
inline char& RC(char &a, char &b){RC(a), RC(b); return a;}
inline char& RC(char &a, char &b, char &c){RC(a), RC(b), RC(c); return a;}
inline char& RC(char &a, char &b, char &c, char &d){RC(a), RC(b), RC(c), RC(d); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e){RC(a), RC(b), RC(c), RC(d), RC(e); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f); return a;}
inline char& RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g){RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g); return a;}
inline DB& RF(DB &a, DB &b){RF(a), RF(b); return a;}
inline DB& RF(DB &a, DB &b, DB &c){RF(a), RF(b), RF(c); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d){RF(a), RF(b), RF(c), RF(d); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e){RF(a), RF(b), RF(c), RF(d), RF(e); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f); return a;}
inline DB& RF(DB &a, DB &b, DB &c, DB &d, DB &e, DB &f, DB &g){RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g); return a;}
inline void RS(char *s1, char *s2){RS(s1), RS(s2);}
inline void RS(char *s1, char *s2, char *s3){RS(s1), RS(s2), RS(s3);}
template<class T0,class T1>inline T0& RDD(T0&a, T1&b){RDD(a),RDD(b); return a;}
template<class T0,class T1,class T2>inline T1& RDD(T0&a, T1&b, T2&c){RDD(a),RDD(b),RDD(c); return a;}
 
template<class T> inline void RST(T &A){memset(A, 0, sizeof(A));}
template<class T> inline void FLC(T &A, int x){memset(A, x, sizeof(A));}
template<class T> inline void CLR(T &A){A.clear();}
 
template<class T0, class T1> inline void RST(T0 &A0, T1 &A1){RST(A0), RST(A1);}
template<class T0, class T1, class T2> inline void RST(T0 &A0, T1 &A1, T2 &A2){RST(A0), RST(A1), RST(A2);}
template<class T0, class T1, class T2, class T3> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3){RST(A0), RST(A1), RST(A2), RST(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);}
template<class T0, class T1> inline void FLC(T0 &A0, T1 &A1, int x){FLC(A0, x), FLC(A1, x);}
template<class T0, class T1, class T2> inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x);}
template<class T0, class T1, class T2, class T3> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);}
template<class T0, class T1, class T2, class T3, class T4> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x){FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x), FLC(A6, x);}
template<class T> inline void CLR(priority_queue<T> &Q){while (!Q.empty()) Q.pop();}
template<class T> inline void CLR(stack<T> &S){while (!S.empty()) S.pop();}
template<class T> inline void CLR(queue<T> &Q){while (!Q.empty()) Q.pop();}
 
template<class T0, class T1> inline void CLR(T0 &A0, T1 &A1){CLR(A0), CLR(A1);}
template<class T0, class T1, class T2> inline void CLR(T0 &A0, T1 &A1, T2 &A2){CLR(A0), CLR(A1), CLR(A2);}
template<class T0, class T1, class T2, class T3> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3){CLR(A0), CLR(A1), CLR(A2), CLR(A3);}
template<class T0, class T1, class T2, class T3, class T4> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);}
template<class T0, class T1, class T2, class T3, class T4, class T5> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);}
template<class T0, class T1, class T2, class T3, class T4, class T5, class T6> inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6){CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);}
template<class T> inline void CLR(T &A, int n){REP(i, n) CLR(A[i]);}
 
template<class T> inline bool EPT(T &a){return a.empty();}
template<class T> inline T& SRT(T &A){sort(ALL(A)); return A;}
template<class T, class C> inline T& SRT(T &A, C cmp){sort(ALL(A), cmp); return A;}
template<class T> inline T& RVS(T &A){reverse(ALL(A)); return A;}
template<class T> inline T& UNQQ(T &A){A.resize(unique(ALL(A))-A.begin());return A;}
template<class T> inline T& UNQ(T &A){SRT(A);return UNQQ(A);}
template<class T, class C> inline T& UNQ(T &A, C cmp){SRT(A, cmp);return UNQQ(A);}
 
 
//}
 
/** Constant List .. **/ //{
 
const int MOD = 998244353;
const int INF = 0x3f3f3f3f;
const LL INFF = 0x3f3f3f3f3f3f3f3fLL;
const DB EPS = 1e-9;
const DB OO = 1e20;
const DB PI = acos(-1.0); //M_PI;
 
const int dx[] = {-1, 1, 0, 0};
const int dy[] = {0, 0, 1, -1};
 
//}
 
/** Add On .. **/ //{
// <<= '0. Nichi Joo ., //{
 
template<class T> inline bool checkMin(T &a,const T b){return b < a ? a = b, 1 : 0;}
template<class T> inline bool checkMax(T &a,const T b){return a < b ? a = b, 1 : 0;}
template <class T, class C> inline bool checkUpd(T& a, const T b, C c){return c(b,a) ? a = b, 1 : 0;}
template<class T> inline T min(T a, T b, T c){return min(min(a, b), c);}
template<class T> inline T max(T a, T b, T c){return max(max(a, b), c);}
template<class T> inline T min(T a, T b, T c, T d){return min(min(a, b), min(c, d));}
template<class T> inline T max(T a, T b, T c, T d){return max(max(a, b), max(c, d));}
template<class T> inline T min(T a, T b, T c, T d, T e){return min(min(min(a,b),min(c,d)),e);}
template<class T> inline T max(T a, T b, T c, T d, T e){return max(max(max(a,b),max(c,d)),e);}
template<class T> inline T sqr(T a){return a*a;}
template<class T> inline T cub(T a){return a*a*a;}
template<class T> inline T ceil(T x, T y){return (x - 1) / y + 1;}
template<class T> T abs(T x){return x>0?x:-x;}
inline int sgn(DB x){return x < -EPS ? -1 : x > EPS;}
inline int sgn(DB x, DB y){return sgn(x - y);}
 
inline DB cos(DB a, DB b, DB c){return (sqr(a)+sqr(b)-sqr(c))/(2*a*b);}
inline DB cot(DB x){return 1./tan(x);};
inline DB sec(DB x){return 1./cos(x);};
inline DB csc(DB x){return 1./sin(x);};
 
//}
// <<= '1. Bitwise Operation ., //{
namespace BO{
 
inline bool _1(int x, int i){return bool(x&1<<i);}
inline bool _1(LL x, int i){return bool(x&1LL<<i);}
inline LL _1(int i){return 1LL<<i;}
inline LL _U(int i){return _1(i) - 1;};
 
inline int reverse_bits(int x){
    x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
    x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
    x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
    x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
    x = ((x >>16) & 0x0000ffff) | ((x <<16) & 0xffff0000);
    return x;
}
 
inline LL reverse_bits(LL x){
    x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
    x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
    x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
    x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
    x = ((x >>16) & 0x0000ffff0000ffffLL) | ((x <<16) & 0xffff0000ffff0000LL);
    x = ((x >>32) & 0x00000000ffffffffLL) | ((x <<32) & 0xffffffff00000000LL);
    return x;
}
 
template<class T> inline bool odd(T x){return x&1;}
template<class T> inline bool even(T x){return !odd(x);}
template<class T> inline T low_bit(T x) {return x & -x;}
template<class T> inline T high_bit(T x) {T p = low_bit(x);while (p != x) x -= p, p = low_bit(x);return p;}
template<class T> inline T cover_bit(T x){T p = 1; while (p < x) p <<= 1;return p;}
template<class T> inline int cover_idx(T x){int p = 0; while (_1(p) < x ) ++p; return p;}
 
inline int clz(int x){return __builtin_clz(x);}
inline int clz(LL x){return __builtin_clzll(x);}
inline int ctz(int x){return __builtin_ctz(x);}
inline int ctz(LL x){return __builtin_ctzll(x);}
inline int lg2(int x){return !x ? -1 : 31 - clz(x);}
inline int lg2(LL x){return !x ? -1 : 63 - clz(x);}
inline int low_idx(int x){return !x ? -1 : ctz(x);}
inline int low_idx(LL x){return !x ? -1 : ctz(x);}
inline int high_idx(int x){return lg2(x);}
inline int high_idx(LL x){return lg2(x);}
inline int parity(int x){return __builtin_parity(x);}
inline int parity(LL x){return __builtin_parityll(x);}
inline int count_bits(int x){return __builtin_popcount(x);}
inline int count_bits(LL x){return __builtin_popcountll(x);}
 
} using namespace BO;//}
 
 
// <<= '2. Number Theory .,//{
namespace NT{
//#define gcd __gcd
inline LL gcd(LL a, LL b){return b?gcd(b,a%b):a;}
inline LL lcm(LL a, LL b){return a*b/gcd(a,b);}
 
inline void INC(int &a, int b){a += b; if (a >= MOD) a -= MOD;}
inline int sum(int a, int b){a += b; if (a >= MOD) a -= MOD; return a;}
 
/* 模数两倍刚好超 int 时。
inline int sum(uint a, int b){a += b; a %= MOD;if (a < 0) a += MOD; return a;}
inline void INC(int &a, int b){a = sum(a, b);}
*/
 
inline void DEC(int &a, int b){a -= b; if (a < 0) a += MOD;}
inline int dff(int a, int b){a -= b; if (a < 0) a  += MOD; return a;}
inline void MUL(int &a, int b){a = (LL)a * b % MOD;}
//inline int pdt(int a, int b){return (LL)a * b % MOD;}
inline int pdt(int x,int y) {
    int ret; __asm__ __volatile__ ("\tmull %%ebx\n\tdivl %%ecx\n":"=d"(ret):"a"(x),"b"(y),"c"(MOD));
    return ret;
}
 
 
inline int gcd(int m, int n, int &x, int &y){
 
    x = 1, y = 0; int xx = 0, yy = 1, q;
 
    while (1){
        q = m / n, m %= n;
        if (!m){x = xx, y = yy; return n;}
        DEC(x, pdt(q, xx)), DEC(y, pdt(q, yy));
        q = n / m, n %= m;
        if (!n) return m;
        DEC(xx, pdt(q, x)), DEC(yy, pdt(q, y));
    }
}
 
inline int sum(int a, int b, int c){return sum(a, sum(b, c));}
inline int sum(int a, int b, int c, int d){return sum(sum(a, b), sum(c, d));}
inline int pdt(int a, int b, int c){return pdt(a, pdt(b, c));}
inline int pdt(int a, int b, int c, int d){return pdt(pdt(a, b), pdt(c, d));}
 
inline int pow(int a, LL b){
    int c(1); while (b){
        if (b&1) MUL(c, a);
        MUL(a, a), b >>= 1;
    }
    return c;
}
 
template<class T> inline T pow(T a, LL b){
    T c(1); while (b){
        if (b&1) c = c * a;
        a = a * a;
        b >>= 1;
    }
    return c;
}
 
template<class T> inline T pow(T a, int b){
    return pow(a, (LL)b);
}
 
inline int _I(int b){
    int a = MOD, x1 = 0, x2 = 1, q; while (1){
        q = a / b, a %= b;
        if (!a) return x2;
        DEC(x1, pdt(q, x2));
 
        q = b / a, b %= a;
        if (!b) return x1;
        DEC(x2, pdt(q, x1));
    }
}
 
inline void DIV(int &a, int b){MUL(a, _I(b));}
inline int qtt(int a, int b){return pdt(a, _I(b));}

} using namespace NT;//}

// <<= '9. Comutational Geometry .,//{
namespace CG{
    
#define cPo const Po&
#define cLine const Line&
#define cSeg const Seg&
    
    inline DB dist2(DB x,DB y){return sqr(x)+sqr(y);}
    
    struct Po{
        DB x,y;Po(DB x=0,DB y=0):x(x),y(y){}
        
        void in(){RF(x,y);}void out(){printf("(%.2f,%.2f)",x,y);}
        inline friend istream&operator>>(istream&i,Po&p){return i>>p.x>>p.y;}
        inline friend ostream&operator<<(ostream&o,Po p){return o<<"("<<p.x<<", "<<p.y<< ")";}
        
        Po operator-()const{return Po(-x,-y);}
        Po&operator+=(cPo p){x+=p.x,y+=p.y;rTs;}Po&operator-=(cPo p){x-=p.x,y-=p.y;rTs;}
        Po&operator*=(DB k){x*=k,y*=k;rTs;}Po&operator/=(DB k){x/=k,y/=k;rTs;}
        Po&operator*=(cPo p){rTs=Ts*p;}Po&operator/=(cPo p){rTs=Ts/p;}
        Po operator+(cPo p)const{return Po(x+p.x,y+p.y);}Po operator-(cPo p)const{return Po(x-p.x,y-p.y);}
        Po operator*(DB k)const{return Po(x*k,y*k);}Po operator/(DB k)const{return Po(x/k,y/k);}
        Po operator*(cPo p)const{return Po(x*p.x-y*p.y,y*p.x+x*p.y);}Po operator/(cPo p)const{return Po(x*p.x+y*p.y,y*p.x-x*p.y)/p.len2();}
        
        bool operator==(cPo p)const{return!sgn(x,p.x)&&!sgn(y,p.y);};bool operator!=(cPo p)const{return sgn(x,p.x)||sgn(y,p.y);}
        bool operator<(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<0;}bool operator<=(cPo p)const{return sgn(x,p.x)<0||!sgn(x,p.x)&&sgn(y,p.y)<=0;}
        bool operator>(cPo p)const{return!(Ts<=p);}bool operator >=(cPo p)const{return!(Ts<p);}
        
        DB len2()const{return dist2(x,y);}DB len()const{return sqrt(len2());}DB arg()const{return atan2(y,x);}
        Po&_1(){rTs/=len();}Po&conj(){y=-y;rTs;}Po&lt(){swap(x,y),x=-x;rTs;}Po&rt(){swap(x,y),y=-y;rTs;}
        Po&rot(DB a,cPo o=Po()){Ts-=o;Ts*=Po(cos(a),sin(a));rTs+=o;}
        
        
        // 求所在象限，大部分情况下只区分两个足够。
        inline int q()const{
            return (y > 0 || y == 0 && x >= 0) ? 0 : 1;
            /*if (x > 0 && y >= 0) return 0;
             if (x <= 0 && y > 0) return 1;
             if (x < 0 && y <= 0) return 2;
             return 3;*/
        }
    };
    
    inline DB dot(DB x1,DB y1,DB x2,DB y2){return x1*x2+y1*y2;}
    inline DB dot(cPo a,cPo b){return dot(a.x,a.y,b.x,b.y);}
    inline DB dot(cPo p0,cPo p1,cPo p2){return dot(p1-p0,p2-p0);}
    inline DB det(DB x1,DB y1,DB x2,DB y2){return x1*y2-x2*y1;}
    inline DB det(cPo a,cPo b){return det(a.x,a.y,b.x,b.y);}
    inline DB det(cPo p0,cPo p1,cPo p2){return det(p1-p0,p2-p0);}
    inline DB ang(cPo p0,cPo p1){return acos(dot(p0,p1)/p0.len()/p1.len());}
    inline DB ang(cPo p0,cPo p1,cPo p2){return ang(p1-p0,p2-p0);}
    inline DB ang(cPo p0,cPo p1,cPo p2,cPo p3){return ang(p1-p0,p3-p2);}
    inline DB dist2(const Po &a, const Po &b){return dist2(a.x-b.x, a.y-b.y);}
    template<class T1, class T2> inline int dett(const T1 &x, const T2 &y){return sgn(det(x, y));}
    template<class T1, class T2, class T3> inline int dett(const T1 &x, const T2 &y, const T3 &z){return sgn(det(x, y, z));}
    template<class T1, class T2, class T3, class T4> inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(det(x, y, z, w));}
    template<class T1, class T2> inline int dott(const T1 &x, const T2 &y){return sgn(dot(x, y));}
    template<class T1, class T2, class T3> inline int dott(const T1 &x, const T2 &y, const T3 &z){return sgn(dot(x, y, z));}
    template<class T1, class T2, class T3, class T4> inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w){return sgn(dot(x, y, z, w));}
    template<class T1, class T2> inline DB arg(const T1 &x, const T2 &y){DB a=ang(x,y);return~dett(x,y)?a:2*PI-a;}
    template<class T1, class T2, class T3> inline DB arg(const T1 &x, const T2 &y, const T3 &z){DB a=ang(x,y,z);return~dett(x,y,z)?a:2*PI-a;}
    template<class T1, class T2, class T3, class T4> inline DB arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w){DB a=ang(x,y,z,w);return~dett(x,y,z,w)?a:2*PI-a;}
    template<class T1, class T2> inline DB dist(const T1 &x, const T2 &y){return sqrt(dist2(x, y));}
    template<class T1, class T2, class T3> inline DB dist(const T1 &x, const T2 &y, const T3 &z){return sqrt(dist2(x, y, z));}
    inline Po _1(Po p){return p._1();}inline Po conj(Po p){return p.conj();}
    inline Po lt(Po p){return p.lt();}inline Po rt(Po p){return p.rt();}
    inline Po rot(Po p,DB a,cPo o=Po()){return p.rot(a,o);}
    inline Po operator *(DB k,cPo p){return p*k;}
    inline Po operator /(DB k,cPo p){return conj(p)*k/p.len2();}
    
    typedef vector<Po> VP;
    
    struct Line{
        Po a,b;Line(cPo a=Po(),cPo b=Po()):a(a),b(b){}
        Line(DB x0,DB y0,DB x1,DB y1):a(Po(x0,y0)),b(Po(x1,y1)){}
        Line(cLine l):a(l.a),b(l.b){}
        
        //Ax+By+C=0
        Line(DB A,DB B,DB C){
            C=-C;if(!::sgn(A))a=Po(0,C/B),b=Po(1,C/B);
            else if(!::sgn(B))a=Po(C/A,0),b=Po(C/A,1);
            else a=Po(0,C/B),b=Po(1,(C-A)/B);
        }
        
        void in(){a.in(),b.in();}
        inline friend istream&operator>>(istream&i,Line& p){return i>>p.a>>p.b;}
        inline friend ostream&operator<<(ostream&o,Line p){return o<<p.a<<"-"<< p.b;}
        
        Line operator+(cPo x)const{return Line(a+x,b+x);}
        Line operator-(cPo x)const{return Line(a-x,b-x);}
        Line operator*(DB k)const{return Line(a*k,b*k);}
        Line operator/(DB k)const{return Line(a/k,b/k);}
        
        Po operator*(cLine)const;
        Po d()const{return b-a;}DB len2()const{return d().len2();}DB len()const{return d().len();}DB arg()const{return d().arg();}
        
        int sgn(cPo p)const{return dett(a, b, p);}
        int sgn(cLine)const;
        
        bool sameSgn(cPo  p1,cPo  p2)const{return sgn(p1)==sgn(p2);}
        void getEquation(DB&K,DB&B)const{
            K = ::sgn(a.x, b.x) ? (b.y-a.y)/(b.x-a.x) : OO;
            B = a.y - K*a.x;
        }
        void getEquation(DB&A,DB&B,DB&C)const{A=a.y-b.y,B=b.x-a.x,C=det(a, b);}
        
        Line&push(DB r){ // 正数右手螺旋向里
            Po v=d()._1().lt()*r;a+=v,b+=v; rTs;
        }
    };
    
    inline DB dot(cLine l1,cLine l2){return dot(l1.d(),l2.d());}
    inline DB dot(cLine l,cPo p){return dot(l.a,l.b,p);}
    inline DB dot(cPo p,cLine l){return dot(p,l.a,l.b);}
    inline DB det(cLine l1,cLine l2){return det(l1.d(),l2.d());}
    inline DB det(cLine l,cPo p){return det(l.a,l.b,p);}
    inline DB det(cPo p,cLine l){return det(p,l.a,l.b);}
    inline DB ang(cLine l0,cLine l1){return ang(l0.d(),l1.d());}
    inline DB ang(cLine l,cPo p){return ang(l.a,l.b,p);}
    inline DB ang(cPo p,cLine l){return ang(p,l.a,l.b);}
    
    inline int Line::sgn(cLine l)const{return dett(Ts, l);}
    inline Po Line::operator*(cLine l)const{return a+d()*det(a,l)/det(Ts,l);}
    inline Po operator&(cPo p,cLine l){return l*Line(p,p+l.d().lt());}
    inline Po operator%(cPo p,cLine l){return p&l*2-p;}
    inline Line push(Line l, DB r){return l.push(r);}
    
    
    struct Seg: public Line{
        Seg(cPo a=Po(),cPo b=Po()):Line(a,b){}
        Seg(DB x0,DB y0,DB x1,DB y1):Line(x0,y0,x1,y1){}
        Seg(cLine l):Line(l){}
        Seg(const Po &a,DB alpha):Line(a,alpha){}
        Seg(DB A,DB B,DB C):Line(A,B,C){}
        
        inline int sgn(cPo p)const;
        inline int sgn(cLine l)const;
        inline bool qrt(cSeg l)const;
        inline int sgn(cSeg l)const;
    };
    
    // -1不相交 0相交（不规范） 1相交（规范）
    
    //inline int Seg::sgn(cPo p)const{return -dott(p,a,b);}
    
    inline int Seg::sgn(cPo p)const{
        if (dett(p, a, b)) return -1; // 有时会有精度误差。。
        if (a == p || b == p) return 0;
        return -dott(p,a,b);
    }
    
    
    inline int Seg::sgn(cLine l)const{return sgn(Ts*l);}
    
    // quick_rejection_test
    inline bool Seg::qrt(cSeg l)const{
        return min(a.x,b.x)<=max(l.a.x,l.b.x)&&min(l.a.x,l.b.x)<=max(a.x,b.x)&&
        min(a.y,b.y)<=max(l.a.y,l.b.y)&&min(l.a.y,l.b.y)<=max(a.y,b.y);
    }
    
    
    inline int Seg::sgn(cSeg l)const{
        if (!qrt(l)) return -1;
        
        /*return
         (dett(a,b,l.a)*dett(a,b,l.b)<=0 &&
         dett(l.a,l.b,a)*dett(l.a,l.b,b)<=0)?1:-1;*/
        
        int d1=dett(a,b,l.a),d2=dett(a,b,l.b),d3=dett(l.a,l.b,a),d4=dett(l.a,l.b,b);
        if ((d1^d2)==-2&&(d3^d4)==-2)return 1;
        return ((!d1&&dott(l.a-a,l.a-b)<=0)||(!d2&&dott(l.b-a,l.b-b)<=0)||
                (!d3&&dott(a-l.a,a-l.b)<=0)||(!d4&&dott(b-l.a,b-l.b)<=0))?0:-1;
    }
    
    //inline DB dist2(cLine l,cPo p){return sqr(fabs(dot(lt(l.d()), p-l.a)))/l.len2();}
    inline DB dist2(cLine l,cPo p){return sqr(fabs(det(l.d(), p-l.a)))/l.len2();}
    
    inline DB dist2(cLine l1,cLine l2){return dett(l1,l2)?0:dist2(l1,l2.a);}
    
    inline DB dist2(cSeg l,cPo p){
        Po pa = p - l.a, pb = p - l.b;
        if (dott(l.d(), pa) <= 0) return pa.len2();
        if (dott(l.d(), pb) >= 0) return pb.len2();
        return dist2(Line(l), p);
    }
    
    
    inline DB dist2(cSeg s,cLine l){
        Po v1=s.a-l.a,v2=s.b-l.a;DB d1=det(l.d(),v1),d2=det(l.d(),v2);
        return sgn(d1)!=sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2)))/l.len2();
    }
    inline DB dist2(cSeg l1,cSeg l2){
        if (~l1.sgn(l2)) return 0;
        else return min(dist2(l2,l1.a), dist2(l2,l1.b), dist2(l1,l2.a), dist2(l1,l2.b));
    }
    template<class T1, class T2> inline DB dist2(const T1& a, const T2& b){
        return dist2(b, a);
    }
    
} using namespace CG;//}

 
 
//}
 
 
 
/** I/O Accelerator Interface .. **/ //{
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x){
    char c;while(!d);x=c-'0';while(d)p;
    return x;
}
template<class T> inline T& RDD(T &x){
    char c;while(g,c!='-'&&!isdigit(c));
    if (c=='-'){x='0'-g;while(d)n;}
    else{x=c-'0';while(d)p;}
    return x;
}
inline DB& RF(DB &x){
    //scanf("%lf", &x);
    char c;while(g,c!='-'&&c!='.'&&!isdigit(c));
    if(c=='-')if(g=='.'){x=0;DB l=1;while(d)nn;x*=l;}
        else{x='0'-c;while(d)n;if(c=='.'){DB l=1;while(d)nn;x*=l;}}
    else if(c=='.'){x=0;DB l=1;while(d)pp;x*=l;}
        else{x=c-'0';while(d)p;if(c=='.'){DB l=1;while(d)pp;x*=l;}}
    return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
inline char* RS(char *s){
    //gets(s);
    scanf("%s", s);
    return s;
}
 
LL last_ans; int Case; template<class T> inline void OT(const T &x){
    //printf("Case #%d: ", ++Case);
    //printf("%lld\n", x);
    //printf("%I64d\n", x);
    //printf("%.9f\n", x);
    //printf("%d\n", x);
    cout << x << endl;
    //last_ans = x;
}

//}/* .................................................................................................................................. */

const int N = int(2e2) + 9;



// <<= '7. Matrix Theory .,//{
namespace MT{

    const int N = 209;
    int n = 0;

    struct matrix{
        int d[N][N];

        void init(int e = 0){RST(d); if(e) REP(i, n) d[i][i] = e;}
        matrix(int e = 0){init(e);}

        matrix operator *(const matrix &rhs) const{
            matrix res; //REP_3(i, j, k, n, n, n) res.d[i][j] += d[i][k] * rhs.d[k][j];
            REP_2(i, j, n, n){
                LL tmp = 0; REP(k, n) tmp += (LL)d[i][k] * rhs.d[k][j];
                res.d[i][j] = tmp % MOD;
            }
            return res;
        }

        matrix& operator *=(const matrix& rhs){return (*this) = (*this) * rhs;}

        inline int res(){
            return d[0][n-1];
        }
        
        void print() {
            REP(i, n) {
                REP(j, n) {
                    cout << d[i][j] << " ";
                }
                cout << endl;
            }
        }
    };

} //using namespace MT;//}

VI adj0[N];
VI adj1[N];

int n, m, k;


void gao() {
    LL a, b; RD(a,b);
    if (a == b) {
        if (a == 1) printf("-1 -1\n");
        else printf("%d %lld\n", 2, max(a, b));
        return;
    }
    LL m = max(a, b);
    int p1 = INF, p2 = -1;
    for (int l = 2, t, r, t2, r2; l <= m; l = r + 1) {
        t = a / l, r = min(m, (t) ? (a / t) : INF);
        t2 = b / l, r2 = min(m, (t2) ? (b / t2) : INF);
        r = min(r, r2);
        if (t != t2 && (a - b) % (t - t2) == 0) {
            int tt =(a - b) / (t - t2);
            if (l <= tt && tt <= r) {
                checkMin(p1, tt);
                checkMax(p2, tt);
            }
        }
    }
    
    if (p1 == INF) p1 = -1;
    printf("%d %d\n", p1, p2);
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("/Users/minakokojima/Documents/GitHub/ACM-Training/Workspace/in.txt", "r", stdin);
    //freopen("/Users/minakokojima/Documents/GitHub/ACM-Training/Workspace/out.txt", "w", stdout);
#endif
    Rush gao();
}